Searching method for maximum-likelihood (ML) detection

ABSTRACT

The present invention relates to a method for searching a solution point of maximum-likelihood detection. The solution point locates at a symbol constellation. The method includes the following steps: determining a central point and a norm by a zero-forcing detection method; determining a searching range according to the central point and the norm; determining at least one qualified solution point according to the searching range; and determining the solution point of maximum-likelihood detection from the qualified solution points.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a wireless communication system, and inparticular, to a multi-input multi-output (MIMO) system for wirelesscommunication.

2. Description of the Prior Art

Recently, due to the rapid increase in the requirements of wirelesscommunication, academic circles and industrial manufacturers have beencontinuously researching transmission methods for highly efficientcommunication. According to basic communication theory, the simplestmethod for achieving highly efficient communication is to increase thebandwidth of signal transmission. As the bandwidth is restricted andlimited, however, it is futile to claim greater efficiency by using avery wide bandwidth to transmit a lot of data. Consequently, a mostinteresting research subject is how to use a plurality of antennas fortransmitting and receiving data under limited bandwidth to achievehighly efficient data communication. That is, in a particularcircumstance with limited bandwidth, the amount of transmitted data canbe raised through increasing the number of transmitting and receivingantennas.

Because different data is assigned to different antennas for transfer atthe same time and at the same bandwidth, these signals transferred bydifferent antennas will obviously interfere with each other at thereceiving end. Therefore, a receiver utilizes a plurality of antennas toreceive signals delivered by a plurality of antennas of a transmitter.As every antenna of the receiver receives signals transferred by adifferent antenna of the transmitter, however, the receiver cannotidentify the signal received by one antenna unless the receiver executessignal processing. Please refer to FIG. 1. Assume a transmitter 10includes M antennas and a receiver 20 includes N antennas. Thetransmitter 10 delivers M symbols X₁, X₂, . . . , X_(M) during onesymbol duration, and then these symbols pass the channel and arereceived by N antennas of the receiver 20. y₁, y₂, . . . y_(N)represents signals received by different antennas at the same time, sothe relationship between a transmission signal, a receiving signal, andthe channel is described through vectors as the following:

$\begin{matrix}{{Y = {{HX} + W}}{wherein}{{Y = \begin{bmatrix}y_{1} \\y_{2} \\\vdots \\y_{N}\end{bmatrix}},{X = \begin{bmatrix}x_{1} \\x_{2} \\\vdots \\x_{M}\end{bmatrix}},{W = \begin{bmatrix}w_{1} \\w_{2} \\\vdots \\w_{N}\end{bmatrix}},{H = \begin{bmatrix}h_{11} & h_{12} & \cdots & h_{1M} \\h_{21} & h_{22} & \cdots & h_{2M} \\\vdots & \vdots & \ddots & \vdots \\h_{N\; 1} & h_{N\; 2} & \cdots & h_{NM}\end{bmatrix}}}} & {{eq}.\mspace{14mu} 1}\end{matrix}$

W represents noise received by N antennas of the receiver 20, and H arepresents signals transmitted by different antennas of the transmitter10 passed to several possible channels to be received by the receiver20. In detail, h_(ij) represents the channel for signal transmissionfrom antenna j of the transmitter 10 to antenna l of the receiver 20,and at the point of communication, symbols X₁, X₂, . . . , X_(M)delivered by the transmitter 10 may be BPSK, QPSK, 4-QAM, 16-QAM, orother modulation types. Consequently, the purpose of the receiver 20 isto properly process the signal Y received by antennas of the receiver 20in order to identify symbols X₁, X₂, . . . , X_(M) delivered by Mantennas of the transmitter 10. Furthermore, related art is disclosed inU.S. Pub. No. 2003/0076890, “method and apparatus for detection anddecoding of signals received from a linear propagation channel” (thisdata is incorporated herein by reference). The related art hassignificant limitations, however.

The receiving end still has the unresolved issue of properly processingthe receiving signal Y received by antennas of the receiver in order toobtain symbols delivered by M transmission antennas.

SUMMARY OF THE INVENTION

Therefore, one objective of the present invention is to provide asearching method for searching a solution point of maximum-likelihood(ML) detection, to solve the above-mentioned problem.

Another objective of the present invention is to provide a searchingmethod for searching a solution point of ML detection that can beapplied in a multi-input multi-output (MIMO) system.

A further objective of the present invention is to provide a searchingmethod for searching a solution point of ML detection, and reducingsearching time.

According to an embodiment of the present invention, a searching methodfor searching a solution point of ML detection is disclosed. Thesolution point locates at a symbol constellation, and the methodincludes: determining a central point and a norm by a zero-forcingdetection method, wherein the solution point of ML detection locatesinside a sphere that utilizes the central point to be a center and thenorm to be a radius; determining a searching range according to thecentral point and the norm; creating at least one qualified solutionpoint according to the searching range; and determining the solutionpoint of ML detection from the qualified solution points.

These and other objectives of the present invention will no doubt becomeobvious to those of ordinary skill in the art after reading thefollowing detailed description of the preferred embodiment that isillustrated in the various figures and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a MIMO communication system with M antennas fortransmission and N antennas for receiving.

FIG. 2 is a diagram of utilizing C_(ZF) to be a radius and {tilde over(X)}₀ to be a central point to search the solution of ML detectionaccording to an embodiment of the present invention.

FIG. 3 is a diagram of the searching range of ML detection, according toan embodiment of the present invention.

DETAILED DESCRIPTION

In general, maximum-likelihood (ML) detection/decoding is considered asan optimal signal detection/decoding method, but due to its complexity,there also exist many sub-optimal detection/decoding methods with lowercomplexity such as the well-known zero-forcing (ZF) detection and MMSEdetection. The present invention utilizes ZF detection aiding MLdetection to reduce the complexity of ML detection. The followingdescription further describes ML and ZF detection.

Briefly, the ML detection/decoding method is represented as{circumflex over (X)} _(ML)=arg{min{|Y−HX| ² }}, Xε{QPSK/QAM}  eq. 2The receiver predicts all possible lattices X delivered by thetransmitter and utilizes eq. 2 to determine which set X (that is, whichlattice X) satisfies eq. 2, to obtain the solution of ML detection{circumflex over (X)}_(ML). In other words, definingC=|Y−HX| ²,  eq. 3the ML detection means that the receiver guesses all possible sets Xdelivered by the transmitter and applies eq. 3 to determine which set Xcreates minimum C, then the set X is the solution of MLdetection/decoding and is labeled as {circumflex over (X)}_(ML).Obviously, ML detection is a highly complex method. For example, everysymbol transferred from the transmitter is modulated by 64-QAM, i.e.there are M symbols in one set X, resulting in the receiver having toguess 64^(M) combinations to obtain the solution of ML detection. It isdifficult to materialize the extremely complex method to commercialproducts without proper simplification. Therefore, some sub-optimalmethods are introduced, such as ZF detection:{tilde over (X)} ₀=(H ^(H) H)⁻¹ H ^(H) Y, {circumflex over (X)}_(ZF)=slicer({tilde over (X)} ₀)  eq. 4

Eq. 4 is utilized while N is greater than M or equal to M, but for thecondition N equals to M, ZF detection has another form:{tilde over (X)} ₀ =H ⁻¹ Y, {circumflex over (X)} _(ZF)=slicer({tildeover (X)} ₀)  eq. 5

Eq. 4 and eq. 5 are both recognized as ZF detection. The followingdescription explains how to utilize ZF detection aiding ML detection torealize a lower complex ML detection/decoding method.

A sphere decoding method is applied to transfer the solution of MLdetection into another form:{circumflex over (X)} _(ML)=arg{min{|Y−HX|²}}≡arg{min(X−{tilde over(X)}₀)^(H) H ^(H) H(X−{tilde over (X)} ₀)}, Xε{QPSK/QAM}  eq. 6In eq. 6, {tilde over (X)}₀ is treated as a central point of a sphere,and the solution of ML detection is a lattice that is nearest to thecentral point. The ML detection searches all lattices X, and finds alattice {circumflex over (X)}_(ML) related to the central point {tildeover (X)}₀ with shortest norm to be the solution of ML detection. Inother words, {circumflex over (X)}_(ML) creates a minimum C in thefollowing equation:C=(X−{tilde over (X)}₀)^(H) H ^(H) H(X−{tilde over (X)}₀)  eq. 7

It is therefore possible to define a proper radius or a norm and use{tilde over (X)}₀ to be a center to construct a sphere. If the norm islong enough, the sphere includes the solution point {circumflex over(X)}_(ML) of ML detection. As mentioned above, the key point is how todetermine a suitable radius or a norm. According to eq. 6, {circumflexover (X)}_(ML) is the solution point of ML detection and is the nearestlattice related to the central point {tilde over (X)}₀. For this reason,the solution of ZF detection (the lattice {circumflex over (X)}_(ZF))must have a norm C_(ZF) related to the central point {tilde over (X)}₀that is longer than (or equal to) the norm C_(ML) between the lattice{circumflex over (X)}_(ML) and the central point {tilde over (X)}₀.Please note that, C_(ZF) and C_(ML), the result of eq. 7 being appliedto {circumflex over (X)}_(ZF) and {circumflex over (X)}_(ML)respectively, results in the following relationship:0≦C_(ML)≦C_(ZF)  eq. 8According to eq. 8, applying {tilde over (X)}₀ to be the central pointand C_(ZF) to be the radius to construct a sphere, guarantees that{circumflex over (X)}_(ML) locates inside the sphere and means thatusers can search the solution of ML detection {circumflex over (X)}_(ML)inside the sphere to simplify the original searching procedures appliedin eq. 2. From a viewpoint of eq. 6, searching procedures of eq. 2 areequivalent to searching for {circumflex over (X)}_(ML) inside a spherewith an unlimited radius, so the complexity is higher than the presentinvention, which searches for {circumflex over (X)}_(ML) in a sphereapplying {tilde over (X)}₀ to be the central point and C_(ZF) to be theradius. Meanwhile, from eq. 4 and eq. 5, the solution point of ZFdetection {circumflex over (X)}_(ZF) is the lattice determined throughmaking a hard decision to the central point {tilde over (X)}₀, andC_(ZF) is the norm between the lattice {circumflex over (X)}_(ZF) andthe central point {tilde over (X)}₀. Hence the method utilizing {tildeover (X)}₀ to be the central point and C_(ZF) to be the radius toconstruct a sphere and searching for the lattice {circumflex over(X)}_(ML) inside the sphere is more efficient.

Due to the prior art utilizing {tilde over (X)}₀ to be a center toconstruct a sphere with a proper radius and then finding the lattice{circumflex over (X)}_(ML) inside the sphere, it is obvious that if theradius is not long enough, the solution point {circumflex over (X)}_(ML)will not be included inside the sphere, so the radius should beincreased to reconstruct a new sphere and searching procedures of thesolution of ML detection {circumflex over (X)}_(ML) should be repeatedagain. On the other hand, the present invention utilizes {tilde over(X)}₀ to be a center and C_(ZF) to be a radius for constructing a sphereand then finds the solution of ML detection {circumflex over (X)}_(ML)inside the sphere. It is therefore guaranteed that {circumflex over(X)}_(ML) locates inside the sphere. Please refer to eq. 8 and FIG. 2;FIG. 2 is a diagram of utilizing C_(ZF) to be a radius and {tilde over(X)}₀ to be a central point to search the solution of ML detectionaccording to an embodiment of the present invention.

Next, how to identify whether the lattice is inside the sphere afterdefining the sphere radius C_(ZF) will be further discussed. Now, theconcept about searching for the solution point inside the sphere isclear, but there is no clear mathematical equation to accomplish thesearching action on the electric circuit.

Through a mathematic operation such as Cholesky factorization in thelinear algebra, eq. 7 is transformed into:C=(X−{tilde over (X)}₀)^(H) H ^(H) H(X−{tilde over (X)}₀)=(X−{tilde over(X)}₀)^(H) U ^(H) U(X−{tilde over (X)}₀)  eq. 9wherein U is an M×M upper triangular matrix. In general, the diagonalelements u_(ii), i=1,2, . . . ,M are all greater than zero. Introducingthe concept of the sphere and the above-mentioned radius C_(ZF), thedesired lattice must satisfy:

$\begin{matrix}\begin{matrix}{C = {\left( {X - {\overset{\sim}{X}}_{0}} \right)^{H}U^{H}{U\left( {X - {\overset{\sim}{X}}_{0}} \right)}}} \\{= {{\sum\limits_{i = 1}^{M}{u_{ii}^{2}{{x_{i} - {\overset{\sim}{x}}_{i} + {\sum\limits_{j = {i + 1}}^{M}{\frac{u_{ij}}{u_{ii}}\left( {x_{j} - {\overset{\sim}{x}}_{j}} \right)}}}}^{2}}} \leq C_{ZF}}}\end{matrix} & {{eq}.\mspace{14mu} 10}\end{matrix}$wherein the central point {tilde over (X)}₀=[{tilde over (X)}₁ {tildeover (X)}₂ . . . {tilde over (X)}_(M)]^(T) andX=[X₁ X₂ . . . X_(M)]^(T), T represent transposition. Referring to eq.10, if only the term i=M is left, the following equation is obtained:

$\begin{matrix}{\left. {{u_{MM}^{2}{{x_{M} - {\overset{\sim}{x}}_{M}}}^{2}} \leq C_{ZF}}\Rightarrow{{{x_{M} - {\overset{\sim}{x}}_{M}}}^{2} \leq \frac{C_{ZF}}{u_{MM}^{2}}} \right. = r_{M}^{2}} & {{eq}.\mspace{14mu} 11}\end{matrix}$Please note that a new radius r_(M) ²=C_(ZF)/u_(MM) ² is defined. Theobject of transforming eq. 10 to eq. 11 is to obtain the solution of MLdetection {circumflex over (X)}_(ML)=[X′_(1,ML) X′_(2,ML) . . .X′_(M,ML)]^(T) from eq. 10. It is necessary to try all possible setsX=[X₁ X₂ . . . X_(M) ]^(T) to find one set {circumflex over(X)}_(ML)=[X′_(1,ML) X_(2,ML) . . . X′_(M,ML)]^(T) such that C has aminimum value C_(ML). From eq. 11, we can determine a searching rangeabout the ML solution X′_(M,ML) of X_(M) delivered by the Mth antenna ofthe transmitter. That is, there may be several X_(M) satisfying eq. 11,and the solution X′_(M,ML) is among these X_(M). For every candidateX_(M) that satisfies eq. 11, eq. 10 can be utilized to obtain two termsi=M−1 and i=M

$\begin{matrix}{{{u_{{({M - 1})}{({M - 1})}}^{2}{{x_{M - 1} - {\overset{\sim}{x}}_{M - 1} + {\frac{u_{{({M - 1})}M}}{u_{{({M - 1})}{({M - 1})}}}\left( {x_{M} - {\overset{\sim}{x}}_{M}} \right)}}}^{2}} + {u_{MM}^{2}{{x_{M} - {\overset{\sim}{x}}_{M}}}^{2}}} \leq C_{ZF}} & {{eq}.\mspace{14mu} 12}\end{matrix}$to find several possible X_(M−1) corresponding to each X_(M) satisfyingeq. 11. Through repeating the procedure recursively until i=1, severalsets X=[X₁ X₂ . . . X_(M)]^(T) will be obtained, and can then be appliedto eq. 9 and eq. 10, to determine the solution set {circumflex over(X)}_(ML)=[X′_(1,ML) X′_(2,ML) . . . X′_(M,ML)]^(T) with minimum C. Butit is still difficult to find all possible X_(M) satisfying eq. 11, soeq. 11 is rewritten as|X_(M)−{tilde over (X)}_(M)|² ≦r _(M) ²  eq. 13a

or:|X _(M) −{tilde over (X)} _(M) |≦r _(M)  eq. 13b

The present invention provides a simplified method to be realized in theelectric circuit. The simplified method utilizes a searching range alittle larger than the original range defined by eq. 13a and eq. 13b tocover the solution point X′_(M,ML).

Because X_(M) utilizes BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, or otherhigh-level modulation methods, X_(M) can be separated into a real partXi_(M) and an imaginary part Xj_(M) respectively. Similarly, {tilde over(X)}_(M) is also separated into a real part {tilde over (X)}i_(M) and animaginary part {tilde over (X)}j_(M), and eq. 13b can be rewritten as:|X _(M) −{tilde over (X)} _(M)|=|(Xi _(M) −{tilde over (X)}i _(M))+j(Xj_(M) −{tilde over (X)}j _(M))|≦r _(M)  eq. 14Utilizing a simple algebra relationship|Xi _(M) −{tilde over (X)}i _(M)|≦|(Xi _(M) −{tilde over (X)}i_(M))+j(Xj _(M) −{tilde over (X)}j _(M))| and|Xj _(M) −{tilde over (X)}j _(M)|≦|(Xi _(M) −{tilde over (X)}i_(M))+j(Xj _(M) −{tilde over (X)}j _(M))|,eq. 14 can be further analyzedto obtain the following relationship:

$\begin{matrix}\left\{ \begin{matrix}{{\left( {{xi}_{M} - {\overset{\sim}{x}i_{M}}} \right)} \leq r_{M}} \\{{\left( {{xj}_{M} - {\overset{\sim}{x}j_{M}}} \right)} \leq r_{M}}\end{matrix} \right. & {{eq}.\mspace{14mu} 15}\end{matrix}$

The solution that satisfies eq. 14 also surely satisfies eq. 15. Pleaserefer to FIG. 3. FIG. 3 is a diagram illustrating the searching range ofML detection according to an embodiment of the present invention.

From FIG. 3, it is obvious that the solution point satisfying eq. 14locates inside a circle. The central point of the circle in FIG. 3 is{tilde over (X)}_(M), due to the solution point satisfying eq. 15locates inside the square (shown in FIG. 3); as the square surrounds thecircle, the solution point satisfying eq. 14 must satisfy eq. 15 too.Originally, we have to find solutions including X′_(M,ML) through eq.14, and it is very complex to realize this on integrated circuits. Bythe method disclosed in the present invention, the searching method istransferred to a simpler method for finding the solution of eq. 15.Taking a 16-QAM modulation illustrated in FIG. 3 for example, thepresent invention constructs a square with the smallest area to exactlysurround the circle, and defines a searching range about the real andimaginary part of the solution X′_(M,ML) through separate projection foraxis I and axis Q. Explicitly speaking, the searching range of X′_(M,ML)on axis I and Q, x′i_(M,ML) and X′j_(M,ML), is limited by the followingequations:┌{tilde over (X)}i _(M) −r _(M) ┐≦Xi _(M) ≦└{tilde over (X)}i _(M) +r_(M)┘  eq. 15a┌{tilde over (X)}j _(M) −r _(M) ┐≦Xj _(M) ≦└{tilde over (X)}j _(M) +r_(M)┘  eq. 15bwherein function ┌ ┐ means a minimum integer not less than the operatedparameter. Similarly, function └ ┘ means a maximum integer not greaterthan the operated parameter. As a result, the solutions satisfying eq.15a must include X′i_(M,ML) and the solutions satisfying eq. 15a mustinclude X′j_(M,ML). Consequently, the present invention provides eq. 15aand eq. 15b for easily completing on circuits through limiting thesearching range of X′_(M,ML) on both axes Q and I. In a preferredembodiment, X′_(M,ML) utilizes separate projection for I and Q torespectively define a searching range, or processes I and Q together forcreating a square on the complex plane to define the searching range ofX′_(M,ML). Furthermore, in the procedure of recursively performingsphere decoding to find remaining X_(M−1), X_(M−2), . . . , X₁, thesearching range is capable of using eq. 15a and eq. 15b to search thesolution of ML detection X_(M−1), X_(M−2), . . . , X₁. Anotherembodiment of the present invention replaces the circle with a square torespectively search the ML solution on axes Q and I. In fact, forrequirements of particular circuit application, the method for searchingX′_(M,ML) on the complex plane through respectively searching I and Q isvariable, i.e. separately defining searching ranges of I and Q. Forexample, shortening the searching range of the axis I to reduce circuitcomplexity, enables the solution point X′_(M,ML) to be searched forinside a rectangle or a square on the complex plane.

Those skilled in the art will readily observe that numerousmodifications and alterations of the device and method may be made whileretaining the teachings of the invention. Accordingly, the abovedisclosure should be construed as limited only by the metes and boundsof the appended claims.

1. A method for identifying a plurality of symbols transmitted by atransmitter of a wireless communication system according to a pluralityof signals received by a receiver of the wireless communication system,the method being implemented in the receiver and for searching asolution point of maximum-likelihood (ML) detection according to theplurality of signals and thereby identifying the plurality of symbols,the method comprising: utilizing a zero-forcing detection to process theplurality of signals and thereby provide a central point; slicing thecentral point to provide a solution point for the zero-forcingdetection; calculating a radius C_(ZF) for the ML detection, the radiusC_(ZF) being the distance between the central point and the solutionpoint for the zero-forcing detection, which consequently results in theradius C_(ZF) longer than or equal to a distance C_(ML) from the centralpoint to a solution point of the ML detection; determining a searchingrange of the ML detection according to the central point and the radiusC_(ZF); determining one or more qualified solution points according tothe plurality of signals and the searching range; and determining one ofthe one or more qualified solution points as the solution point of theML detection.
 2. The method of claim 1, wherein the searching range is asphere, the central point and the radius C_(ZF) define the sphere, andthe ML detection utilizes a sphere decoding method.
 3. The method ofclaim 1, wherein the searching range is a rectangle.
 4. The method ofclaim 3, wherein the central point is a geometric center of therectangle and both length and width of the rectangle are not shorterthan double the radius C_(ZF).
 5. The method of claim 1, wherein thesearching range is a square.
 6. The method of claim 5, wherein thecentral point is a geometric center of the square and each side lengthof the square is not shorter than double the radius C_(ZF).
 7. Themethod of claim 1, wherein the receiver of the wireless communicationsystem has a plurality of antennas for receiving the signals.
 8. Themethod of claim 1, wherein the slicing comprises rounding eachcoordinate of the central point to a nearest integer.
 9. The method ofclaim 1, wherein the solution point of the zero-forcing detection is apoint that is on a zero-forcing lattice.
 10. The method of claim 9,wherein the central point is a point that is not on the zero-forcinglattice.
 11. The method of claim 1, wherein the central point is anintermediate unrounded result of zero-forcing detection.
 12. A wirelesscommunication receiver, comprising: logic that utilizes a zero-forcingdetection to process a plurality of signals received from a transmitterand thereby provide a central point; logic that slices the central pointto provide a solution point for the zero-forcing detection; logic thatcalculates a radius C_(ZF) for a maximum-likelihood (ML) detection, theradius C_(ZF) being the distance between the central point and thesolution point for the zero-forcing detection; logic that determines asearching range of the ML detection according to the central point andthe radius C_(ZF); and logic that determines at least one qualifiedsolution point for the ML detection according to the plurality ofsignals and the searching range.